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POSITIVE SOLUTIONS FOR FRACTIONAL BOUNDARY VALUE PROBLEMS UNDER A GENERALIZED FRACTIONAL OPERATOR

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The work reported here concerns with study a generalized nonlinear fractional boundary value problems involving ϑ-fractional derivative in the Riemann-Liouville sense. The existence and uniqueness of positive solutions to the… Click to show full abstract

The work reported here concerns with study a generalized nonlinear fractional boundary value problems involving ϑ-fractional derivative in the Riemann-Liouville sense. The existence and uniqueness of positive solutions to the problem at hand are proved. Our discussion relies on the properties of the Green's function, the upper and lower solutions method, and the classical fixed point theorems in a cone. Moreover, building upper and lower control functions have an effective role in the analysis. Some examples are offered to justify the validity of theoretical findings.

Keywords: positive solutions; solutions fractional; boundary value; fractional boundary; value problems

Journal Title: Mathematical Methods in The Applied Sciences
Year Published: 2021

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